A pulse doppler radar partitions each range cell within its footprint into doppler cells. Synthetic aperture radar imaging includes two major steps: processing each footprint, as in the pulse doppler radar to obtain a map of reflectivity versus range and doppler, and transferring and accumulating the reflectivity information of each footprint onto an absolute x--y reflectivity map, one doppler cell after the other. This second step is denoted as mapping. In the classical synthetic aperture radar (SAR) the antenna illuminates a sideway footprint while following a horizontal linear trajectory at constant velocity. Since the footprint is moving, each scatterer appears to move with respect to the range cell boundaries. This phenomenon which is called range walk is critical, because a pulse doppler radar requires that the scatterers remain within the same range cell during the entire observation interval (D.sub.ob). For the linear geometry of the classical SAR, the range walk effect is small. Therefore, the SAR can operate with a sufficiently large observation interval to achieve a high doppler resolution, and consequently a high azimuth resolution. The mapping of a trapezoidal azimuth cell, corresponding to a doppler cell, onto the absolute x--y reflectivity map is easily performed on the basis of geometric considerations, because all the footprints are the same except for a translation.
However, for a nonlinear geometry, range walk increases and the range walk constraint reduces the observation interval to such an extent that classical SAR is not practical. To extend SAR imaging to nonlinear geometries range walk must be reduced to extend the applicability of pulse doppler radars, and a mapping method must be used which works even when the size, shape, and orientation of the azimuth cells varies. By using range relative doppler processing and invariant mapping these problems can be resolved.
Standard pulse radars divide the beam into N.sub.R range cells. Pulse doppler radars transmit a sequence of N.sub.P pulses during the observation interval. For each transmitted pulse, N.sub.R pairs of in phase and quadrature samples are collected, one pair for each range cell. At the end of the observation interval, the raw data is stored in an information matrix of size N.sub.P .times.N.sub.R. Each scatterer generates N.sub.P return pulses during the observation interval. Assume that there are several scatterers within a range cell. Then, a Fourier analysis on the combined data for this range cell (one row of the information matrix) allows discrimination between the scatterers if their doppler difference is greater than the frequency resolution .DELTA.f=1/D.sub.ob. The main constraint for the pulse doppler radar is that the scatterers remain within the same range cell during the entire observation interval D.sub.ob. In the case of nonlinear geometries, the range walk due to the relative motion between scatterers and targets increases as does the doppler bias. It follows that the observation interval has to be reduced to satisfy the range walk constraint and that the doppler increment .DELTA.f increases to such an extent that the performance of the pulse doppler radar becomes unacceptable. The classical synthetic aperture radar also called sidelooking radar, is an advanced pulse doppler radar which includes mapping. The most common application is to generate a ground map of reflectivity versus absolute x--y coordinates through analysis of the data collected by an antenna which provides a sideway illumination while following a linear horizontal trajectory at constant velocity. At the center of the observation interval, the beam defines a footprint on the ground. A map of reflectivity versus range and doppler is generated for the footprint in the same manner as noted hereinabove for the pulse doppler radar. Then, the footprint information is transferred to and accumulated on an x--y reflectivity map, one trapezoidal azimuth cell at a time. This procedure, called mapping of all the footprints is completed, an estimated x--y reflectivity map is computed by averaging of the information from the overlapping footprints. In the classical SAR, mapping is based on geometric considerations because the size and shape of the azimuth cells remains the same.